Aircraft: B757
Phase of flight: Initial Approach
Anomaly: Inflight Event / Encounter CFTT / CFIT; Inflight Event / Encounter Weather / Turbulence

I was the pilot flying. On arrival cleared initially the FIORA 4 [and] given vector direct to PARZA. The weather was heavy with thunderstorms all around the airport; even though they were calling better than 1;500 and 7 KM. I looked at the performance pages; which showed we could land on Runway 07 with the wind they were calling; essentially 15 KTS of tailwind; runway wet. Our approach speed was about 119 KIAS. Due to weather I requested direct to TOMAS and proceeded DCT there. We were cleared for the VOR 07 circle to land on Runway 25. Once we were cleared for the approach (APP) I selected LOC and captured the localizer; I also had the VOR selected to TIO and course 068 for the VOR; but we never changed the FMC to reflect the VOR APP instead of the ILS APP. While both are essentially the same course; about the same path; the same MIN ALT over CARBA and MONTE; and the same missed APP Procedure; and I felt we could have just followed the same guidance; I wanted to correct the FMC. When we changed the FMC and entered the VOR 07; we extended from the wrong point and ended up with only the extension from the MA point. While I had deviated slightly north of course to avoid the worst of the weather; I corrected to back on course between CARBA and MONTE. I continued to follow the course on raw data; and respect the altitudes; and I had the ILS data as a back up (we had inquired if the ILS was working properly). We had just passed CARBA 6;000A; and were short of MONTE 4;600A (probably about 4;900 FT) when we got the EGPWS 'TERRAIN' CAUTION message. With everything else going on (weather; wrong FMC APP; and now the warning) I decided to do an ESCAPE maneuver. Once we started climbing (very fast as we were very light) we went right through a heavy thunderstorm I started a left turn towards the west and informed ATC we were going west and that we needed a climb to 12;000 FT. While we were in the turn we got another EGPWS WARNING 'TERRAIN PULL UP' so we continued the escape maneuver until we were heading west and above 12;000 FT. We requested DCT to LIB and 18;000 FT; and diverted. In retrospect; I should have never accepted the VOR APP Circle to land on Runway 25 given the weather conditions surrounding the MROC airport. I should have also discontinued the approach once I realized we had the wrong approach loaded into the FMC instead of trying to salvage it. Captain and I were flying the FIORA 4 STAR into San Jose; Costa Rica. We had anticipated the ILS 07 approach though the reported wind was westerly; we were not exceeding the 15 KT tailwind requirement for landing on Runway 07. Approaching the airport we discovered the weather was not exactly as reported--there were numerous cells between us and the airport and the wind had increased to a reported 18 KTS or so still out of the west. We were subsequently issued the VOR DME Runway 07 approach circle to Runway 25 and accepted it. We; also at the time of receiving the clearance; were fighting to avoid numerous cells; moderate rain and very turbulent conditions. Captain asked that I ask ATC for a turn towards TOMAS on the approach to avoid a cell ahead and we were granted that clearance. Things happened fast from here on out. We attempted to switch the FMC to the appropriate approach (ILS vs. VOR DME); but failed to do so correctly and in a timely manor. We did observe that the fixes and altitudes on both approaches were the same and knew that we were in safe parameters of the approach corridor and still quickly attempted to draw an extended centerline from MONTE inbound; but were unable to successfully do that. It was then descending to 4;600 FT at MONTE that at approximately 4;900 FT we received an EGPWS 'CAUTION TERRAIN' alert and Captain immediately performed an escape maneuver. We climbed and turned left to head west to safer terrain and shortly thereafter (around 5;500 FT?) received a 'TERRAIN; TERRAIN; PULL UP' Ground Proximately Warning. We continued to climb; ending up at 18;000 and diverted.On looking back at these events; I think we should have; perhaps held inbound after receiving the circle clearance to Runway 25 and set up and briefed it all more completely. Weather; turbulence; unforecasted IMC conditions and being issued a new approach are really not conducive to a stable; safe approach procedure. B757 flight crew describes an approach into MROC with thunderstorms and with a last minute change from the ILS 07 to the VOR 07 circle to land Runway 25. A mistake is made modifying the VOR approach in the FMC and the approach is flown in raw data until an EGPWS Terrain caution is announced approaching MONTE at 4;900 FT. The escape maneuver is flown with a turn to the north then to the west as an EGPWS Terrain warning sounds. The crew climbs to 18;000 FT and diverts.